Generation of elliptically polarized attosecond pulses in mixed gases

We propose and theoretically demonstrate a scheme to generate elliptically polarized attosecond pulses with mixed gases. As the harmonic radiations from different gases with opposite orbital parity interfere destructively for one helicity component and constructively for the other, the high-order harmonics from the mixture exhibit large ellipticity with the same helicity in a wide spectral range. Hence, highly elliptically polarized attosecond pulses can be generated from the mixed gases and the ellipticity can be tuned by controlling the mixing ratio and the molecular alignment angle. Furthermore, this interference effect is only related to the features of the mixed gases such as the structure and orbital symmetry of the molecules and atoms. The polarization control is independent of the temporal profile manipulation of the attosecond pulses by shaping the driving field. Consequently, our work paves an effective and convenient way to produce elliptically polarized isolated attosecond pulses with mixed gases by optimizing the polarization and temporal profile individually.

Figure 1

Schematic for the interference in mixed gases based on the rotation vector method, where complex values are represented as vectors in the complex plane. The horizontal axis corresponds to the real axis and the vertical axis corresponds to the imaginary axis. $d_{x,y}^{m,a}$ is the recombination dipole moment projected onto the $x/y$ direction. $d_{\pm }^{m,a}=(d_x^{m,a}\pm i{d}_y^{m,a})/\sqrt{2}$ is the right- and left-rotating component. The superscripts $a$ and $m$ represent the atom and molecule, respectively.

Figure 2

High-order-harmonic spectra from (a) Ar and (b) ${\mathrm{N}}_2$. The blue solid and yellow dashed lines represent the harmonic spectra for the right-rotating component $I_R$ and the left-rotating component $I_L$, respectively. The insets are the ground states of the Ar atom and ${\mathrm{N}}_2$ molecule.

Figure 3

High-order-harmonic spectra for the (a) left- and (b) right-rotating components from Ar (red solid lines) and ${\mathrm{N}}_2$ (blue dashed lines), respectively. (c) The relative phase between high-order-harmonic radiation from Ar and ${\mathrm{N}}_2$ for the left-rotating harmonic components ($\mathrm{\Delta }{\varphi }_L$, blue squares) and the right-rotating harmonic components ($\mathrm{\Delta }{\varphi }_R$, purple circles). (d) High-order-harmonic spectra from Ar-${\mathrm{N}}_2$ mixed gases for the left-rotating component ($I_L$, blue dash-dotted line) and right-rotating component ($I_R$, purple solid line), respectively.

Figure 4

The ellipticity of high-order harmonics from mixed gases as a function of harmonic order and the molecular alignment angle.

Figure 5

The results considering the molecular alignment distribution. (a) The relative phase between high-order-harmonic radiation from Ar and ${\mathrm{N}}_2$ for the left-rotating harmonic components ($\mathrm{\Delta }{\varphi }_L$, blue squares) and right-rotating harmonic components ($\mathrm{\Delta }{\varphi }_R$, purple circles). (b) High-order-harmonic spectra from Ar-${\mathrm{N}}_2$ mixed gases for the left-rotating component ($I_L$, blue dash-dotted line) and right-rotating component ($I_R$, purple solid line), respectively. The laser parameters are the same as those in Fig. 3.

Figure 6

The results considering the multiple orbital contribution. (a) High-order-harmonic spectra from HOMO (blue dashed lines) and HOMO-1 (red solid lines) of ${\mathrm{N}}_2$. (b) High-order-harmonic spectra from Ar-${\mathrm{N}}_2$ mixed gases for the left-rotating component ($I_L$, blue dash-dotted line) and the right-rotating component ($I_R$, purple solid line), with the contributions of both HOMO and HOMO-1 considered for ${\mathrm{N}}_2$. The laser parameters are the same as those in Fig. 3.

Figure 7

The ellipticity of high-order harmonics from mixed gases as a function of harmonic order and the intensity of the driving laser field.

Figure 8

The three-dimensional plot of the electric field for the synthesized attosecond-pulse train with the high-order harmonics from mixed gases. The ellipticity of the attosecond-pulse train is $\varepsilon \approx 0.76$.

Figure 9

Results from Ar-${\mathrm{N}}_2$ mixed gases driven by a few-cycle laser field. (a) The relative phase between high-order-harmonic radiation from Ar and ${\mathrm{N}}_2$ for the left-rotating harmonic components ($\mathrm{\Delta }{\varphi }_L$, blue squares) and right-rotating harmonic components ($\mathrm{\Delta }{\varphi }_R$, purple circles). (b) High-order-harmonic spectra from Ar-${\mathrm{N}}_2$ mixed gases for the left-rotating component ($I_L$, blue dash-dotted line) and right-rotating component ($I_R$, purple solid line), respectively. (c) Time-frequency distribution of the high-order harmonics under the few-cycle laser field. The color map represents the high-order-harmonic intensity in the logarithmic scale. (d) The three-dimensional plot of the electric field for the synthesized isolated attosecond pulse with the high-order harmonics from mixed gases. The ellipticity of the isolated attosecond pulse is about 0.81 and the pulse duration is about 300 as.

Figure 10

Results of the calculation with TDSE. High-order-harmonic spectra for the (a) left- and (b) right-rotating components from Ar (red solid lines) and ${\mathrm{N}}_2$ (blue dashed lines), respectively. (c) The relative phase between high-order-harmonic radiation from Ar and ${\mathrm{N}}_2$ for the left-rotating harmonic components ($\mathrm{\Delta }{\varphi }_L$, blue squares) and right-rotating harmonic components ($\mathrm{\Delta }{\varphi }_R$, purple circles). (d) High-order-harmonic spectra from Ar-${\mathrm{N}}_2$ mixed gases for the left-rotating component ($I_L$, blue dash-dotted line) and right-rotating component ($I_R$, purple solid line), respectively. The laser parameters are the same as those in Fig. 3.